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We consider the problem of joint three-dimensional (3D) localization and material classification of unresolved space debris using a multispectral rotating point spread function (RPSF). The use of RPSF allows one to estimate the 3D locations of point sources from their rotated images acquired by a single 2D sensor array, since the amount of rotation of each source image about its x, y location depends on its axial distance z. Using multispectral images, with one RPSF per spectral band, we are able not only to localize the 3D positions of the space debris but also classify their material composition. We propose a three-stage method for achieving joint localization and classification. In stage 1, we adopt an optimization scheme for localization in which the spectral signature of each material is assumed to be uniform, which significantly improves efficiency and yields better localization results than possible with a single spectral band. In stage 2, we estimate the spectral signature and refine the localization result via an alternating approach. We process classification in the final stage. Both Poisson noise and Gaussian noise models are considered, and the implementation of each is discussed. Numerical tests using multispectral data from NASA show the efficiency of our three-stage approach and illustrate the improvement of point source localization and spectral classification from using multiple bands over a single band.

There is a growing interest in using so-called dynamic functional connectivity, as the conventional static brain connectivity models are being questioned. Brain network analyses yield complex network data that are difficult to analyze and interpret. To deal with the complex structures, decomposition/factorization techniques that simplify the data are often used. For dynamic network analyses, data simplification is of even greater importance, as dynamic connectivity analyses result in a time series of complex networks. A new challenge that must be faced when using these decomposition/factorization techniques is how to interpret the resulting connectivity patterns. Connectivity patterns resulting from decomposition analyses are often visualized as networks in brain space, in the same way that pairwise correlation networks are visualized. This elevates the risk of conflating connections between nodes that represent correlations between nodes' time series with connections between nodes that result from decomposition analyses. Moreover, dynamic connectivity data may be represented with three-dimensional or four-dimensional (4D) tensors and decomposition results require unique interpretations. Thus, the primary goal of this article is to (1) address the issues that must be considered when interpreting the connectivity patterns from decomposition techniques and (2) show how the data structure and decomposition method interact to affect this interpretation. The outcome of our analyses is summarized as follows. (1) The edge strength in decomposition connectivity patterns represents complex relationships not pairwise interactions between the nodes. (2) The structure of the data significantly alters the connectivity patterns, for example, 4D data result in connectivity patterns with higher regional connections. (3) Orthogonal decomposition methods outperform in feature reduction applications, whereas nonorthogonal decomposition methods are better for mechanistic interpretation.

Exposure to acute stress induces multiple emotional responses, each with their own unique temporal dynamics. Dynamic functional connectivity (dFC) measures the temporal variability of network synchrony and captures individual differences in network neurodynamics. This study investigated the relationship between dFC and individual differences in emotions induced by an acute psychosocial stressor. Sixteen healthy adult women underwent fMRI scanning during a social evaluative threat (SET) task, and retrospectively completed questionnaires that assessed individual differences in subjectively experienced positive and negative emotions about stress and stress relief during the task. Group dFC was decomposed with parallel factor analysis (PARAFAC) into 10 components, each with a temporal signature, spatial network of functionally connected regions, and vector of participant loadings that captures individual differences in dFC. Participant loadings of two networks were positively correlated with stress-related emotions, indicating the existence of networks for positive and negative emotions. The emotion-related networks involved the ventromedial prefrontal cortex, cingulate cortex, anterior insula, and amygdala, among other distributed brain regions, and time signatures for these emotion-related networks were uncorrelated. These findings demonstrate that individual differences in stress-induced positive and negative emotions are each uniquely associated with large-scale brain networks, and suggest that dFC is a mechanism that generates individual differences in the emotional components of the stress response. Hum Brain Mapp 38:6185-6205, 2017. © 2017 Wiley Periodicals, Inc., (© 2017 Wiley Periodicals, Inc.)